As a process using cumene as a raw material for reaction, there are known a process having steps of converting cumene into cumene hydroperoxide and obtaining propylene oxide from such cumene hydroperoxide and propylene, aprocess of converting cumene into cumene hydroperoxide and obtaining phenol and acetone by subjecting such cumene hydroperoxide to acidolysis, and the like. In those processes, there is a reaction producing 2,3-dimethyl-2,3-diphenylbutane by dimerizing cumene as an undesirable side-reaction. By-production of 2,3-dimethyl-2,3-diphenylbutane causes undesirable effects such as consumption of cumene and obstruction to a desired reaction.